A multi-pass cavity or cell is an optical device, in which light bounces between mirrors a number of times in at least one stable orbit before exiting the system. A traditional multi-pass cell has a fairly complex structure that typically includes a glass tube, two large aperture mirrors, two end assemblies, and one base plate. Two concave, highly reflective mirrors are mounted on the end assemblies, through which one can adjust the distance between the mirrors. Inside the cell, a laser beam undergoes multiple reflections between the mirrors and traces out dense patterns at the mirror surfaces. The path length, and likewise the beam pattern, can be adjusted by changing the distance between the two mirrors. This design principle was first introduced in 1942. Since then, a variety of multi-pass cells have been developed such as Herriott cells, modified White cells, and improved Herriott cells, but the cell architecture and basic design strategy, based on integrable dynamics under the condition of paraxial ray approximations, remain almost the same. In contrast, non-integrable systems support more variable and complex dynamics with chaos, mixed-mode resonances, or scar modes. Some chaotic non-integrable cavities, such as deformed cylinders and deformed spheres, have been used as laser cavities, multi-pass optical cavities, and cavity ring-down resonators. Nevertheless, previous experimental and theoretical studies have mostly focused on cavities that retain some axial symmetry.
A highly compact Herriott cell can achieve an 11.7 m path length in a cell volume of 42 cm3, and a recently-developed cylindrical mirror multi-pass cell can realize a 174-pass orbit with a mirror separation of only 7.32 cm. However, these systems have two limitations. First, when the cavity is further miniaturized so that the mirror radius is comparable with the size of the spot pattern, the paraxial ray approximation becomes insufficient, as the approximation cannot precisely predict the ray dynamics any more. Second, the alignment of the conventional multi-pass systems is nontrivial: 1) due to the multiple focusing components, and 2) the un-avoidable adjustment of the intermirror spacing. Because these systems require regular intermirror alignment, they are not suitable for unattended field deployment.
One application of interest for the multi-pass cell is as a gas sensor. In a gas sensor, the gas sample is contained in the multi-pass cell and a laser beam is directed through the gas which absorbs laser light at specified wavelengths. The type of molecular species in the cell is identified by observing the wavelength of the energy absorbed. Since the sensitivity of an absorption experiment generally increases with the optical path length and since the measurement response time correlates with the volume of a multi-pass cell, the capability of achieving a long optical path in a small cell volume is especially desired in laser absorption spectroscopy. That is, to accomplish a substantial absorption, a long optical path is generally required. A multi-pass cell is therefore an often used component for gas sensing systems; its optical path length determines the sensitivity and the cell volume critically affects the response time.
In the context of gas sensing, existing multi-pass cells have several drawbacks. First, a typical cell is around 1000 cm3 in volume, which lengthens the cell response time corresponding to the time needed to replace the gas in the cell. Second, high precision in mirror manufacturing is required, which makes systems rather expensive. Third, vibrations or misalignments of the mirrors deteriorate the accuracy of spectrometric measurements. A complicated mirror alignment process and need for maintenance is a particular requirement in gas sensing applications. Therefore, traditional multi-pass cells are not suitable for low cost, compact, and portable gas sensing applications.
Recently, a design strategy was proposed to overcome the limitations of paraxial approximations and intermirror alignments in conventional multi-pass cells by taking advantage of quasi-chaotic ray dynamics in a single closed-surface cavity. (E. Narimanov, J. A. Fan, and C. Gmachl, Tech. Digest. Quantum Electronics and Laser Science Conference (QELS) 1, 421 (2005).) Such a chaotic cavity generally shows a mixture of stable, quasi-chaotic, and chaotic regions in the corresponding phase space. Any ray trajectories, once injected into the stable or quasi-chaotic regions, can be confined within the same region for a long time, whether they obey the paraxial approximation or not. Similar behavior has been studied in deformed dielectric spheres and microcylindrical chaotic cavities. Since quasi-chaotic ray trajectories are sensitive to their initial conditions, varying the initial conditions of the input beam can produce various ray trajectories. Furthermore, the quasi-chaotic multi-pass cell is easier to align and fabricate. Compared with the White cell and Herriott cell, which consist of at least two separate mirrors, the chaotic multi-pass cell has only one mirror. The single mirror enables straightforward alignment due to the closed structure that makes the intermirror alignment unnecessary. Moreover, the closed cavity structure favors manufacture by using either traditional (molding and milling) or advanced (stereolithography) fabrication techniques.
The challenge in designing quasi-chaotic multi-pass cells is to control the tendency of the chaotic beam to diverge. The initial design presented in Narimanov is a one-dimensionally deformed quadrupole sphere, defined as R=R0(1+ε cos 2θ) in the standard spherical coordinates (R, φ, θ), where R0 is the average radius and ε is the deformation parameter. This cavity is featured with a rotationally symmetric structure in the φ direction. However, the beam size of the optical orbit in such a cavity grows linearly in the θ-direction due to the axial symmetry of the device, which leads to uncontrolled chaos in the symmetric direction.
In view of the above, it would be an advance in the state of the art of multi-pass cells and optical gas sensing to develop multi-pass cells which are compact in size, are less susceptible to vibrations and mirror misalignment, and do not suffer from uncontrolled chaos.